The Gaussian free field and SLE(4) on doubly connected domains

Understand

The level lines of the Gaussian free field are known to be related to SLE(4).

• It is shown how this relation allows to define chordal SLE(4) processes on doubly connected domains, describing traces that are anchored on one of the two boundary components.
• The precise nature of the processes depends on the conformally invariant boundary conditions imposed on the second boundary component.
• Extensions of Schramm's formula to doubly connected domains are given for the standard Dirichlet and Neumann conditions and a relation to first-exit problems for Brownian bridges is established.